Question
To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk 34 meters south and 41 meters east. To the nearest meter, how many meters would be saved if it were possible to walk through the pond?
Hint:
Pythagoras' theorem states that “In a right-angled triangle, the square of the hypotenuse side is equal to the sum of squares of the other two sides“. The sides of this triangle have been named Perpendicular, Base and Hypotenuse. Here, the hypotenuse is the longest side, as it is opposite to the angle 90°.
If a is the perpendicular, b is the base, and c is the hypotenuse, then according to the definition, the Pythagoras Theorem formula is given as
c2= a2 + b2
The correct answer is: the meters saved if it were possible to walk through the pond is 19.74 m.
In the given question,
Length of perpendicular(a) = 34 m
Length of base(b) = 41 m
Let’s say that the length of the shortest path is given as d and here the shortest path is the hypotenuse of the right-angled triangle.
Using Pythagoras theorem
d2 = a2 + b2
d2 = 342 + 412
d2 = 2837
d = 
= 53.26 m
Distance travelled to reach point B from A = 34 + 41 = 75 m
The meters saved if it were possible to walk through the pond = 75 - 53.26 = 19.74 m
Final Answer:
Hence, the meters saved if it were possible to walk through the pond is 19.74 m.
= 53.26 mDistance travelled to reach point B from A = 34 + 41 = 75 m
The meters saved if it were possible to walk through the pond = 75 - 53.26 = 19.74 m
Final Answer:
Hence, the meters saved if it were possible to walk through the pond is 19.74 m.
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Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
Volunteers at an animal shelter are building a rectangular dog run so that one shorter side of the rectangle is formed by the shelter building as shown. They plan to spend between $100 and $200 on fencing for the sides at a cost of $2.50 per ft. write and solve a compound inequality to model the possible length of the dog run.
Follow the same steps as when solving equations to solve compound inequalities. However, because compound inequalities are composed of two inequalities, separate them and solve each inequity separately. Once the inequalities are separated, isolate the variable using the inverse operation, similar to how equations are solved.
For example, to solve the compound inequality 14 > 2x > 4, do the following:
14 > 2x > 4
The two inequalities are separated by 14 > 2x and 2x > 4.
To isolate the variable, divide both sides by 2: 14/2 > 2x/2 and 2x/2 > 4/2.
7 > x and x > 2 are now two sets of solutions.
7 > x > 2, the possible answers range from 2 to 7.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
A peanut company ships its product in a carton that weighs 20 oz when empty. Twenty bags of peanuts are shipped in each carton. The acceptable weight for one bag of peanuts is between 30.5 oz and 33.5 oz, inclusive. If a carton weighs too much or too little, it is opened for inspection. Write and solve a compound inequality to determine x, the weight of cartons that are opened for inspection
The compound inequality statement for the weight of inspected cartons is 630 > X > 690. Here, It can also explain like this:
¶Empty carton weight = 20 oz.
Acceptable weight range per bag of peanuts:
The lower limit is 30.5 oz.
Maximum weight = 33.5 oz
20 bags = 20 peanut bags per carton
Therefore,
The following is the lower limit for carton weight after filling:
630 oz = weight of empty carton + (20 * weight per bag) 20 + (20 * 30.5)
The maximum weight of a carton after it has been filled will be:
Empty carton weight + (20 * weight per bag) 20 + (20 * 33.5) = 690 oz
As a result, the compound inequality for the inspected cartons is: 630 > X > 690.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
Fatima plans to spend at least $15 and at most $ 20 on sketch pads and pencils. If she buys 2 sketch pads, how many pencils can she buy while staying in her price range?
Inequalities define the relationship between two non-equal values. Inequality means not being equal. In mathematics, there are five inequality symbols: greater than symbol (>), less than symbol (<), greater than or equal to a sign (≥), less than or equal to a symbol (≤), and not equivalent to a symbol (≠). Many can solve simple inequalities in math by multiplying, dividing, adding, or subtracting both sides until left with the variable.
The compound inequality in this question is solved with the following instructions:
• Let us suppose Fatima purchased 'n' pens.
• Calculating the total money spent on the pens.
• Then solve the inequality by subtraction and division on all sides.
• As a result, you get the answer to how much Fatima spends on pencils while staying within her price range.
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Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
Write a compound inequality to represent the sentence below:
A Quantity x is either less than 10 or greater than 20.
An inequality with a linear function included is referred to as a linear inequality. When the word "and" connects two inequalities, the solution takes place when both inequalities hold true at the same moment. The solution, however, only applies when one of the two inequalities is true when the two are connected by the word "or." The combination or union of the two separate solutions is the solution. When two simple inequalities are combined using either "AND" or "OR," the result is a compound inequality.
One of the two claims is proven to be true by the compound inequality with "AND." If the answers to the separate statements of the compound inequality overlap. While "Or" means that the entire compound sentence is true as long as either of the two statements is true. The solution sets for the various statements are united to form this concept.
Which word has long a sound ?
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Write a compound inequality to represent the sentence below: A Quantity x is at least 10 and at most 20.
Write a compound inequality to represent the sentence below: A Quantity x is at least 10 and at most 20.
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure.
9 ≤ A ≤ 12
Here is a list of some key points to remember when studying triangle inequality:
• The Triangle Inequality theorem states that the sum of any two sides of a triangle must be greater than the sum of the third side.
• In a triangle, two arcs will intersect if the sum of their radii is greater than the distance between their centres.
• If the sum of any two sides of a triangle is greater than the third, the difference of any two sides will be less than the third.
The value for area A of each figure is given. Write and solve a compound inequality for the value of x in each figure.
9 ≤ A ≤ 12
Here is a list of some key points to remember when studying triangle inequality:
• The Triangle Inequality theorem states that the sum of any two sides of a triangle must be greater than the sum of the third side.
• In a triangle, two arcs will intersect if the sum of their radii is greater than the distance between their centres.
• If the sum of any two sides of a triangle is greater than the third, the difference of any two sides will be less than the third.
